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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Statement of the Problem
1.3 Objectives of the Study
1.4 Research Questions
1.5 Significance of the Study
1.6 Scope and Limitations of the Study

Chapter 2: Literature Review
2.1 Overview of Quantum Groups
2.2 Generalized Symmetries of Quantum Groups
2.3 Algebraic Structures in Quantum Groups
2.4 Applications of Quantum Groups in Physics and Mathematics

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Sampling Methods
3.5 Ethical Considerations

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison with Existing Literature
4.3 Implications of the Findings
4.4 Future Research Directions

Chapter 5: Conclusion and Summary
5.1 Summary of key Findings
5.2 Conclusions drawn from the Study
5.3 Recommendations for Future Research
5.4 Contribution to the Field of Algebraic Theory of Quantum Groups

Brief Overview:

The thesis on Algebraic Theory of Quantum Groups at Roots of Unity explores the mathematical structures and properties of quantum groups, with a particular focus on their behavior at roots of unity. Quantum groups are non-commutative algebraic structures that generalize the concept of symmetry from classical groups. This thesis aims to provide a comprehensive overview of the algebraic theory of quantum groups and their applications in physics and mathematics.

The introduction sets the stage by providing background information on quantum groups and outlining the research objectives and questions. The literature review delves into previous research on quantum groups, highlighting key concepts such as generalized symmetries and algebraic structures. The research methodology section details the approach taken to collect and analyze data for the study.

The discussion of findings section presents an analysis of the results, comparing them with existing literature and outlining their implications. The conclusion and summary chapter summarizes the key findings of the study, draws conclusions, and provides recommendations for future research in the field.

Overall, this thesis contributes to the understanding of quantum groups and their behavior at roots of unity, offering insights into their algebraic structures and potential applications in various disciplines.

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